Experimental Techniques in Mineral and Rock Physics

On December 10–11, 1992, a symposium entitled “Experimental Techniques in Mineral and Rock Physics” was held during the Fall 1992 Meeting of the American Geophysical Union in memory of Edward Schreiber. This symposium dramatized the growth and importance of the field of experimental geophysics which was nurtured in its infancy by researchers like Edward Schreiber. The symposium was convened by two former students and colleagues of Schreiber, Robert C. Liebermann and Carl H. Sondergeld.

Ed Schreiber’s life was taken suddenly and tragically on the morning of November 11, 1991 as he was driving to work on the Bronx River Parkway. He was on his way to Queens College, an institution with which he had had a long and valuable association. Ed was born in Brooklyn in 1930. He attended the New York State College of Ceramic Engineering at Alfred University where he received his B.S. degree Magna Cum Laude in 1956 and his Ph.D. degree in 1963. As a graduate student, Ed was inspired by both Taro Takahashi and Orson Anderson.

Dissolution of plagioclase under the physical conditions at shallow to intermediate burial depths is a prime candidate for secondary porosity generation in feldspathic siliciclastic sediments. The diagenetic behavior of granular aggregates of plagioclase feldspar and quartz has been investigated by experimentation performed in a Bridgeman-type pressure vessel. The experiments, each of two weeks duration, simulated pressure-temperature conditions approximating 3.5 km burial depth. By using a double-acting pore-fluid reservoir, solutions of various chemistries were cycled through samples composed of oligoclase or labradorite feldspar and quartz (90:10 wt% respectively).

Scanning electron microscope analysis of the post-experiment samples reveals dissolution features and precipitated products. Dissolution voids of ∼ 10 microns occur typically in areas of maximum stress such as crack-tips and grain contacts. Dissolution on a larger scale is exemplified by topographical smoothing of grain surfaces. The dissolved species are subsequently reprecipitated as Ca-enriched overgrowths (possibly zeolites) and clays. These precipitates are found individually on the scale of 10 microns and collectively as surface coatings on both feldspar and quartz grains. Atomic absorption spectroscopic analyses of the pore fluid suggest that the fluid chemistry is consistent with the observed experimental precipitates.

These experiments show that clay coatings are unnecessary precursors to grain surface dissolution and that the diagenetic precipitation is not mineral selective. Also, the mass transfer of the dissolved species appears to be localized because grains displaying both dissolution and precipitation features are commonplace. Volume changes due to mineral transformation/alteration may increase secondary porosity if the dissolved species produced from dissolution are only partially involved in reprecipitation and the remaining dissolved material is flushed out by the pore fluids. However, if the mass transfer is primarily local then permeability would significantly decrease as precipitates may choke the pore throats.

We will describe a new laboratory system which was designed to be highly automated and portable while maintaining quality. Driving this design was the recognition of the temporal dependence of physical properties. It becomes apparent that some sedimentary rocks, particularly shales, degrade and disaggregate so completely that mechanical or elastic properties cannot be measured. This temporal dependence displays a time scale much shorter than normal weathering but greater than the time for stress relief. A system was designed to permit field characterization of freshly recovered core material. A benefit of automation and portability is a marked increase in measurement efficiency. The attributes of this system permit rapid characterization of a large number of fresh cores in remote, frontier exploration areas. This feature can significantly reduce prospect evaluation time. Statistically significant rock property databases can be created in a short period of time.

The constitutive equations of poroelasticity contain four static moduli. Different sets of moduli are reviewed in the context of their laboratory measurement and their geophysical applications. One complete set consists of the drained bulk modulus and Poisson’s ratio, and their undrained counterparts. Skempton’s coefficient (ratio of pore pressure increment to mean stress increment under undrained conditions) and the Biot-Willis parameter serve equally well for the undrained bulk modulus and Poisson’s ratio, because they permit the drained and undrained moduli to be related to each other. Time dependence is introduced into poroelastic behavior through Darcy’s law. Geophysical applications that can be approximated by undrained conditions (fast loading) include seismicity, tidal and barometric loading, and tectonic compression. Several of these problems are most directly formulated in terms of Skempton’s coefficient, undrained Poisson’s ratio, and hydraulic diffusivity.

Compressional and shear-wave velocities (V _p and V _s ) of 210 minicores of carbonates from different areas and ages were measured under variable confining and pore-fluid pressures. The lithologies of the samples range from unconsolidated carbonate mud to completely lithified limestones. The velocity measurements enable us to relate velocity variations in carbonates to factors such as mineralogy, porosity, pore types and density and to quantify the velocity effects of compaction and other diagenetic alterations.

Pure carbonate rocks show, unlike siliciclastic or shaly sediments, little direct correlation between acoustic properties (V _p and V _s ) with age or burial depth of the sediment so that velocity inversions with increasing depth are common. Rather, sonic velocity in carbonates is controlled by the combined effect of depositional lithology and several post-depositional processes, such as cementation or dissolution, which results in fabrics specific to carbonates. These diagenetic fabrics can be directly correlated to the sonic velocity of the rocks.

At 8 MPa effective pressure V _p ranges from 1700 to 6500 m/s, and V _s ranges from 800 to 3400 m/s. This range is mainly caused by variations in the amount and type of porosity and not by variations in mineralogy. In general, the measured velocities show a positive correlation with density and an inverse correlation with porosity, but departures from the general trends of correlation can be as high as 2500 m/s. These deviations can be explained by the occurrence of different pore types that form during specific diagenetic phases. Our data set further suggests that commonly used correlations like “Gardner’s Law” (V _p -density) or the “time-average-equation” (V _p -porosity) should be significantly modified towards higher velocities before being applied to carbonates.

The velocity measurements of unconsolidated carbonate mud at different stages of experimental compaction show that the velocity increase due to compaction is lower than the observed velocity increase at decreasing porosities in natural rocks. This discrepancy shows that diagenetic changes that accompany compaction influence velocity more than solely compaction at increasing overburden pressure.

The susceptibility of carbonates to diagenetic changes, that occur far more quickly than compaction, causes a special velocity distribution in carbonates and complicates velocity estimations. By assigning characteristic velocity patterns to the observed diagenetic processes, we are able to link sonic velocity to the diagenetic stage of the rock.

To obtain the temperature T and volume V (or pressure P) dependence of the Anderson-Grüneisen parameter δ _T , measurements with high sensitivity are required. We show two examples: P, V, T measurements of NaCl done with the piston cylinder and elasticity measurements of MgO using a resonance method. In both cases, the sensitivity of the measurements leads to results that provide information about δ _T (η, T), where η ≡ V/V ₀ and V ₀ is the volume at zero pressure. We demonstrate that determination of δ _T leads to understanding of the volume and temperature dependence of q = (∂ ln γ/∂ ln V) _T over a broad V, T range, where γ is the Grüneisen ratio.

A new giga-Hertz ultrasonic interferometer has been developed, based on ultrasonic microscopy technology. The interferometer operates from 0.3 GHz to 1.5 GHz. The high frequency and associated small wavelengths together with the large bandwidth make it possible to measure travel times in samples with thicknesses of several microns and allow for unprecedented accuracy in bond corrections. An absolute accuracy of 1 part in 10⁵ in travel time measurements is achievable in single crystals (thickness of ∼200 microns) or glasses of interest to the earth sciences. The high precision travel time data, combining with sample length measurements using a laser interferometer built in our laboratory, yield very high precision ultrasonic velocities.

The interferometer is intended for use in conjunction with a newly developed 4 GPa gas piston cylinder apparatus (Getting and Spetzler, 1993) for equation of state measurements under simultaneous pressure and temperature. A separate correction for the bond will be made for each datum at every point in temperature pressure space.

The complete travel-time equation of state (CT-EOS) is presented by utilizing thermodynamics relations, such as;

The CT-EOS enables us to analyze ultrasonic experimental data under simultaneous high pressure and high temperature without introducing any assumption, as long as the density, or thermal expansivity, and heat capacity are also available as functions of temperature at zero pressure. The performance of the CT-EOS was examined by using synthesized travel-time data with random noise of 10⁻⁵ and 10⁻⁴ amplitude up to 4 GPa and 1500 K. Those test conditions are to be met with the newly developed GHz interferometry in a gas medium piston cylinder apparatus. The results suggest that the combination of the CT-EOS and accurate experimental data (10⁻⁴ in travel time) can determine thermodynamic and elastic parameters, as well as their derivatives with unprecedented accuracy, yielding second-order pressure derivatives (∂² M/∂P ²) of the elastic moduli as well as the temperature derivatives of their first-order pressure derivatives (∂² M/∂P ∂T). The completeness of the CT-EOS provides an unambiguous criterion to evaluate the compatibility of empirical EOS with experimental data. Furthermore because of this completeness, it offers the possibility of a new and absolute pressure calibration when X-ray (i. e., volume) measurements are made simultaneously with the travel-time measurements.

We present new elasticity measurements on single-crystal fayalite and combine our results with other data from resonance, pulse superposition interferometry, and Brillouin scattering to provide a set of recommended values for the adiabatic elastic moduli C _ij and their temperature variations. We use a resonance method (RPR) with specimens that were previously investigated by pulse superposition experiments. The nine C _ij of fayalite are determined from three new sets of measurements. One set of our new C _ij data is over the range 300–500 K. We believe that the relatively large discrepancies found in some C _ij are due in large part to specimen inhomogeneities (chemical and microstructural) coupled with differences in the way various techniques sample, rather than only systematic errors associated with experimental procedures or in the preparations of the specimens.

Our recommended C _ij ’s (GPa) and (∂C _ij /∂T) _p (GPa/K) are:

The resulting values for the isotropic bulk and shear moduli, K _s and μ, and their temperature derivatives are: K _s = 134(4) GPa; μ = 50.7(0.3) GPa; (∂K _s /∂T) _P = −0.024(0.005) GPa/K; and (∂μ/ ∂T) _P = −0.013(0.001) GPa/K. An important conclusion is that K _s increases as the Fe/(Fe + Mg) ratio in olivine is increased.

At moderate temperatures, the elastic properties of natural MgAl₂O₄ spinel differ in several significant ways from properties of synthetic spinels. Below 1000 K, the ultrasonic resonant frequencies of an ordered natural spinel change significantly after heat treatment; at higher temperatures, both types of spinels have similar resonant responses. The temperature derivatives of the elastic constants of an ordered spinel also differ from those of disordered spinels at moderate temperatures; again, at higher temperatures, both types of spinels have similar behaviors. The Raman spectra also differ below 1000 K for ordered natural and disordered spinels and are similar at higher temperatures and after cooling to ambient temperature. We associate these changes in ultrasonic resonance and Raman spectra of spinel with cation disordering at high temperature which may be quenched by cooling. We deduce estimates of the inversion parameter from the relative intensities of the two A_lg Raman modes in very good agreement with estimates made from other measurements. We find that C ₁₁ and C ₁₂ decrease by 4 and 8%, respectively, with 20% inversion in spinel; C ₄₄ is less sensitive to cation order. These results imply that previous measurements of the adiabatic elastic constants of spinels at ambient conditions have been affected by the state of cation disorder of the specimen.

An apparatus is described which provides for the investigation of viscoelasticity/anelasticity in geologic and related materials under conditions of high pressure and temperature. Cylindrical specimens are tested in torsion — a geometry particularly well suited to shear mode observations at the low strain amplitudes of the linear regime. Forced oscillation experiments allow the measurement of dispersion and attenuation at the low frequencies of teleseismic wave propagation. The conduct of complementary forced oscillation and creep tests allows recoverable anelastic strains to be distinguished from those of permanent viscous deformation. It has been demonstrated that robust measurements can be made at strain amplitudes below 10⁻⁵ and frequencies of 1 mHz−1 Hz, under P-T conditions to 300 MPa and 1200°C. The prospects for further development of this facility are outlined.

In the 1960s, E. Schreiber and his colleagues pioneered the use of hot-pressed polycrystalline aggregates for studies of the pressure and temperature dependence of the elastic wave velocities in minerals. We have extended this work to the high-pressure polymorphs of mantle minerals by developing techniques to fabricate large polycrystalline specimens in a 2000-ton uniaxial split-sphere apparatus. A new cell assembly has been developed to extend this capability to pressures of 20 GPa and temperatures of 1700°C. Key elements in the new experimental design include: a telescopic LaCrO₃ for T > 1200°C; Toshiba Tungaloy grade F tungsten carbide anvils; and the use of homogeneous glasses or seeded powder mixtures as starting material to enhance reactivity and maximize densities. Cell temperatures are linearly related to electrical power to 1700°C and uniform throughout the 3 mm specimens. Pressure calibrations at 25°C and 1700°C are identical to 15 GPa. Cylindrical specimens of the beta and spinel phases of Mg₂SiO₄, stishovite (SiO₂-rutile), and majorite-pyrope garnets have been synthesized within their stability fields in runs of 1–4 hr duration and recovered at ambient conditions by simultaneously decompressing and cooling along a computer-controlled P-T path designed to preserve the high-pressure phase and to relax intergranular stress in the polycrystalline aggregate. These specimens are single-phased, fine-grained (<5 micron), free of microcracks and preferred orientation, and have bulk densities greater than 99% of X-ray density. The successful fabrication of these high-quality polycrystalline specimens has made possible experiments to determine the pressure dependence of acoustic velocities in the ultrasonics laboratory of S. M. Rigden and I. Jackson at the Australian National University.

The new hydrothermal diamond anvil cell (HDAC) has been designed for optical microscopy and X-ray diffraction at pressures up to 10 GPa and temperatures between −190°C and 1200°C. Laser light reflected from the top and bottom anvil faces and the top and bottom solid sample faces produce interference fringes that provide a very sensitive means of monitoring the volume of sample chamber and for observing volume and refractive index changes in solid samples due to transitions and reactions. Synchrotron radiation has been used to make X-ray diffraction patterns of samples under hydrothermal conditions. Individual heaters and individual thermocouples provide temperature control with an accuracy of ±0.5°C. Liquid nitrogen directly introduced into the HDAC has been used to reduce the sample temperature to −190°C. The α−β phase boundary of quartz has been used to calculate the transition pressures from measured transition temperatures. With this method we have redetermined 5 isochores of H₂O up to 850°C and 1.2 GPa at which the solution rate of the quartz became so rapid that the quartz dissolved completely before the α−β transition could be observed. When silica solutions were cooled, opal spherules and rods formed.

A new technique actively controls thermal radiation and monitors sample properties during laser-heating in a diamond anvil cell. The technique can be described as a qualitative application of thermal analysis. Discontinuities in temperature, laser power, visible thermal radiation, or in their derivatives as functions of time can be associated with the enthalpy of phase transitions (such as melting) or with changes in material properties (such as emissivity).

The technique is illustrated with melting experiments on iron-magnesium-silicate perovskite. Temperature corrections associated with these experiments are discussed and the results are briefly reviewed.

Deviatoric stress in a diamond anvil cell with gold as a pressure and stress indicator is measured by two complementary techniques using synchrotron radiation. The first method employs a white X-ray beam using energy dispersive X-ray diffraction. The incident X-ray beam is parallel to the load axis and the diffraction pattern is recorded at a low two-theta angle. Using powder diffraction patterns of polycrystalline gold, we measured the elastic strain of two crystal planes oriented normal to the diffraction vector. Stresses nearly parallel and perpendicular to the load axis can be calculated by stress-strain tensor relationship. The other method uses a monochromatic wiggler X-ray beam. In this case, the diamond cell is oriented so that the incident beam is perpendicular to the load axis. The diffraction pattern is recorded on an image plate area detector. Elastic strains responding to stresses perpendicular and parallel to the load axis can be measured and stresses of the same orientations can be calculated from the strain data. These measurements provide a lower bound of the actual differential stresses in a diamond cell. With these techniques, we can measure stress distribution in a less deviatoric gasketted sample and determine yield strength of mantle materials at high pressures and temperatures.

New and improved techniques and apparatus for testing the mechanical properties of materials at high pressures and temperatures are described. These include an improved Griggs-type deformation apparatus designed to operate to 5 GPa and associated servo-controlled hydraulic drive and electronics, the design of hydrostatic (molten alkali halide mixtures) pressure assemblies to measure flow stresses as low as a few MPa, the characterization of temperature gradients and friction in such assemblies, measurement of the melting curve of an alkali halide mixture used as a confining pressure medium, and the measurement of acoustic emissions.

Uniaxial compressive stress-strain curves have been measured on a suite of 26 commercial grades of tungsten carbide cermets and three maraging steels of interest for use in high-pressure apparatus. Tests were conducted on cylindrical specimens with a length to diameter ratio of two. Load was applied to the specimens by tungsten carbide anvils padded by extrudable lead disks. Interference fit binding rings of maraging steel were pressed on to the ends of the specimens to inhibit premature corner fractures. Bonded resistance strain gages were used to measure both axial and tangential strains. Deformation was exremely uniform in the central, gauged portion of the specimens. Tests were conducted at a constant engineering strain rate of 1 × 10⁻⁵ S^−l. The composition of the specimens was principally WC/Co with minor amounts of other carbides in some cases. The Co weight fraction ranged from 2 to 15%. Observed compressive strengths ranged from about 4 to just above 8 GPa. Axial strain amplitude at failure varied from ∼ 1.5% to ∼9%. Representative stress-strain curves and a ranking of the grades in terms of yield strength and strain at failure are presented. A power law strain hardening relation and the Ramberg-Osgood stress-strain equation were fit to the data. Fits were very good for both functions to axial strain amplitudes of about 2%. The failure of these established functions is accompanied by an abrupt change in the trend of volumetric strain consistent with the onset of substantial microcrack volume.

The rheological properties of mantle materials are being investigated up to pressures of 16 GPa and temperatures of 1600°C for times up to 24 h, using a new sample assembly for the 6–8 multi-anvil apparatus. Al₂O₃ pistons, together with a liquid confining medium, are used to generate deviatoric stress in the specimen. Strain rates are estimated by monitoring the relative displacement of the guide blocks of the multi-anvil apparatus, scaled to the total axial strain of the sample. The applied stress on the sample is estimated using grain size piezometry. Strain rates and flow stresses of approximately 10⁻⁴ to 10⁻⁶ s−1 and 50 to 250 MPa respectively, are presently attainable.

Preliminary results on San Carlos olivine single crystals, partially dynamically recrystallized to a grain size of 10 to 300 μm, indicate that the effective viscosity of polycrystalline olivine is consistent with values obtained from olivine single crystal creep laws. Assuming a dislocation creep mechanism (n ≈ 3.5) with (010)[001] as the dominant slip system, the data are best fit using a creep activation volume of 5 to 10 × 10⁻⁶m³mol⁻¹.

A new multi-anvil type high-presure apparatus has been developed using sintered diamond anvils to generate pressures over 30 GPa and temperatures up to about 2000°C. A maximum sample volume of about 1 mm³ is available in this system. The pressure was confirmed by dissociation of forsterite into Mg-perovskite and periclase. The basic techniques and problems in utilizing sintered diamond in the MA8 type high-pressure apparatus are discussed with an emphasis on the future prospect of incorporating simultaneous X-ray diffraction observation.

We have designed and calibrated a piston-cylinder cell assembly suitable for conducting in situ measurements of enthalpies of phase transitions at elevated pressures by heat-flux differential scanning calorimetry (DSC). The high-pressure DSC detector consists of a Pt-Ptl3%Rh thermopile wrapped around a frame of fired pyrophyllite. Four thermocouple junctions, arranged radially around the sample capsule, are connected in series, with four reference thermocouple junctions located 3–4 mm above the sample and embedded in thermally inert ceramic. A W-W25%Re control thermocouple is situated directly above the top of the sample; the whole detector assembly is enclosed in a 1.5 mm thick cylindrical ceramic sleeve located at the center of a 8–10 mm long “hot-zone” in the tapered graphite furnace. Using this detector design and cell assembly, we have observed the thermal signal associated with the fusion of Au at 0.5 and 1.2 GPa, and have calculated a calibration factor (K) for this detector based on the gold melting curve of Mirwald and Kennedy (1979). Detector sensitivity decreases by a factor of four over this pressure-temperature interval. The reproducibility of the enthalpy of fusion of gold at 0.5 GPa suggests that detector geometry is reproducible from one experiment to the next, and thus confirms the viability of this particular detector design for quantitative DSC measurements. Subsequent experiments will assess the dependence of (K) on temperature and pressure by measuring the enthalpies of fusion of additional metals (e. g., Ag, Cu, Al, Ge) and salts (e. g., NaCl, CsCl).

Few diffusion coefficient values have been measured for silicate minerals at pertinent geologic conditions because of experimental restrictions. Until recently, analysis of diffusion couples was conducted principally with electron microprobes which have rather poor spatial resolution (micrometer scale). Ion microprobe analyses, however, eliminate many of the previous experimental restrictions; in depth profile mode they have excellent spatial resolution (tens of angstroms) and diffusion couples can be analyzed normal to the interface. Diffusion couples analyzed by ion microprobe must be well-defined and uniform; previous methods using solution precipitates to form the diffusion couples were heterogeneous and had limited success. A new approach, the thermal evaporation of ²⁵MgO under high vacuum onto a crystalline substrate (oxide, silicate), produces a 1000 Å thick ²⁵MgO _x (x < 1) thin film. This method yields an excellent diffusion couple for low-temperature diffusion experiments. Diffusion anneal experiments using this approach for garnet provide a Mg self-diffusion coefficient of D = 0.60 ± 0.09 × 10⁻²¹ m²/s at 1000°C (logfO₂ = −11.3, P = 1 atm, X _Almandine = 0.24).

Pressure behavior of ZnTe at room temperature was studied using an X-ray energy dispersive method on a DIA type cubic anvil apparatus (SAM-85) at NSLS-X17B1. By using powdered polyethylene, the sample and NaCl for a pressure scale were held under quasihydrostatic conditions, which were confirmed by X-ray diffraction method. Two high-pressure phase transitions were confirmed using X-ray powder diffraction simultaneously with electrical resistance measurements. The phase transition pressures under quasihydrostatic conditions were determined to be 9.6 GPa, at which the resistance increased, and 12.0 GPa, which was the midpoint of a large resistance decrease. Errors in the pressure determinations were estimated to be less than 0.2 GPa. These pressure values may depend on grain size and anisotropic stress effects on the calibrant. From X-ray observation of ZnTe, the bulk modulus of the zinc blende structure was calculated to be K ₀ = 51(3) GPa and K′₀ = 3.6(0.8), and the first transition at 9.6 GPa was found to have about 9% volume change. It was consistent with an anomaly in the pressure generating curves.

A new method for making gas-tight seals for moderate temperature duty on triaxial deformation apparatus sample columns is described. This includes the modification of the piston and closure plug to enable rapid and inexpensive changes to the loading column.0